RHV Controller described near conflict and confused event when clearing a departure from Runway 13R; when thinking the clearance was from Runway 13L; reporter noted a required clearance read back may have prevented situation.

Narrative

I was working Local 1 position when Aircraft X called Tower ready for takeoff while holding short of Runway 13L. I said to Aircraft X 'make a straight out departure; Runway 13R cleared for takeoff without delay; traffic turning left base' when I meant to clear Aircraft X for takeoff on Runway 13L. Aircraft X read back Runway 13R cleared for takeoff; I did not catch the read back and Aircraft X proceeded across Runway 13L. When I noticed Aircraft X crossing Runway 13L I instructed him to hold short of Runway 13R. Aircraft X did not read back the hold short instructions and I immediately told Aircraft X cancel takeoff clearance. Aircraft X did not read back the cancel takeoff clearance and I physically observed Aircraft X clear Runway 13L and hold short of runway 13R while I instructed Aircraft Y who previously landed on Runway 13R to hold short of Runway 13L due to the landing traffic. After Aircraft Y read back hold short of Runway 13L and was clear of Runway 13R; I cleared Aircraft X for takeoff on Runway 13R. I used my controller judgment when I did not ask Aircraft X to read back hold short of Runway 13R and cancel takeoff clearance because I observed no immediate danger in the runway environment and another transmission to get the two read backs from Aircraft X would have congested the frequency when I was instructing Aircraft Y to hold short of Runway 13L due to the landing traffic. No loss of separation. Recommendation; I recommend that I get complete read back hold short instructions from pilots before I give them a takeoff clearance even if the transmission will cause a short delay and even if I physically observe the aircraft hold short of the assigned destination.